Jessen’s Inequality and Exponential Convexity Of Positive Semigroups On Banach Lattice Algebra

A classical theory of fundamental inequalities and positive definiteness is presented in [1, 2]. In the present note, a Jessen inequality for strongly continuous positive semigroups is proved. Which is followed by the results regarding positive definiteness and exponential convexity of operators in a semigroup. Key words. Positive semigroups on Banach lattices, Means of Cauchy’s type, Positive semi-definiteness, Exponential convexity.